Wednesday, January 16, 2013

Probability vs. likelihood

Probability -- a function of the outcome given a fixed parameter value. (What's the probability that 50 heads will come up, given that I toss a fair coin (--> parameters) 50 times?)Likelihood -- a function of the parameters given a fixed outcome. (What's the likelihood a coin is fair if 50 heads came up out of 100 (--> outcome)?)
The likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values.